Extensional flows dominate industrial processes, however, the response of materials in such flow fields are poorly understood. This is mostly attributed to the difficulty in designing an apparatus to strictly measure extensional properties.
Whereas several instruments are commercially available to measure the shear properties of such complex fluids, there are very few commercially available instruments for the measurement of extensional properties. The working principle of an extensional rheometer is analogous to the shear (torsional) rheometer. In a shear rheometer, a quantity of sample is placed between two plates (flat, coned, annular, etc.) and one or both plates are rotated at a constant rate, stress, or oscillated at a prescribed frequency. Through careful measurement of the torque required to rotate the disk(s) or the resulting strain of the material given a prescribed torque, it is possible to determine a shear viscosity as a function of stress, strain, or frequency.
The same concepts apply to an extensional rheometer. However, instead of applying a simple shear flow between two plates, the extensional rheometer applies a stretching flow. The principle underlying extensional flow is that a sample is stretched such that its cross sectional area is decreasing in time. Here lies the difficulty in applying a well-defined extensional flow, since applying a constant extensional strainrate or stress to a material requires controlling how the material's cross sectional area is changing in time. This is fundamentally different than a shear rheometer, where the cross sectional area is constant in time.
The majority of materials made from polymers have properties that are neither completely solid-like (elastic) nor completely fluid-like (viscous). These materials are often referred to as “soft” materials or “complex” fluids (“complex” due to their complex molecular structure). From a mechanical perspective these materials are referred to as viscoelastic. A complete description of viscoelasticity is far from complete, however, in the limit of small deformations, i.e. close to equilibrium, there exists a framework called the theory of linear viscoelasticity. In this limit, a material has precisely the same rheological response in both shear and extension. Therefore, this limit acts as a superb test for the working principle of any design of an extensional rheometer. Outside the small deformation limit, known as the nonlinear viscoelastic response, which is more relevant to industrial processing flows, shear and extensional rheological properties are fundamentally different and in some cases completely opposite, i.e., shear thinning and extension thickening. Thus the nonlinear shear properties of complex fluids alone are insufficient and irrelevant to characterizing, predicting, and controlling complex fluids in industrially relevant flows. Therefore, a technique that can measure accurately and quantitatively the linear and nonlinear viscoelastic extensional properties of complex materials would be invaluable.
Despite academic and industrial interests and attempts in measuring extensional properties of complex fluids, very few methods are commercially available that provide absolute quantitative parameters. Most methods do not actively monitor the strain of material and instead correlate strain from a mechanical motion. This assumption is not always valid, prevents the ability to obtain steady state rheological properties, and can easily lead to erroneous irreproducible results.
In so-called filament stretching rheometers (FSR), the strain is a direct measurement via in-situ measurement of the mid-filament diameter via optical techniques. There have been many designs over the years to ensure the measurement of the mid-filament diameter.
One solution has been to design an FSR with an optical measuring device to a fixed diameter measuring point, from where both plates moved symmetrically. Another solution has been to equip an FSR with an optical measuring device to a moving stage, and linking this to the movement of one of the plates, such that only the mid-filament diameter was measured.
The mid-filament diameter, which per se is the diameter measured mid between the two plates, can be used to determine rheological properties, in ideal cases where mid-filament diameter is the minimum diameter. For some materials, this is indeed the case, but for polymer melts and solutions, this is not always the case. Due to gravity, the minimum diameter may be below the mid-filament diameter. This effect is referred to as the sagging effect. By measuring the mid-filament diameter, where sagging occurs, the rheological properties may be miscalculated.
What is missing is a device, in particular an FSR, for measuring theological properties of materials, in particular polymer melts and solutions, where the sagging effect is taken into account.
Furthermore, in FSRs, measuring or knowing the strain is not enough. For an extensional rheometer to be useful it must be capable of prescribing a well-defined rheological flow, such as constant uniaxial extension and/or constant stress. In the working principle of the FSR, a movement of the plates, suspending the material, correlates to a decrease or increase of the diameter. This correlation/relationship depends on the material being measured, the measurement temperature and the strain-rate or stress applied. Not surprisingly, this correlation/relationship is almost never known a priori: making it very difficult to apply a well-defined rheological flow.
Two approaches have been taken to overcome this hurdle. The first method uses an open-loop control scheme to determine the correlation/relationship, while the second method avoids it using a closed loop feedback control. FSR designs that use open-loop feedback control require a great deal of experimental iteration: wasting sample and time.
FSR designs that use closed-loop feedback control require a link between the measured mid-filament diameter and the movement. If the mid-filament diameter however is different from the minimum diameter, according to the sagging effect, the rheological flow may end up being wrong.
What is missing is an FSR with closed-loop control with the ability to measure a variety of extensional rheological properties of complex fluids where the sagging effect is taken into account.